We do see food supply making its way into Gotham which could as well have been shared with the trapped cops as we see food being given to the police as well. I can't really explain more than what we see in film.

Yes...there is one scene that shows supplies coming into the city. There are a couple of scenes with Drake sneaking messages into the trapped cops. But nothing shows supplies going to them. Now....people will say - You have to assume that they are being fed. Really? How much? The Viet Cong fed the American prisoners of war they had....and they almost starved to death. Do you think that Bane was sending tons of food down to the men that he planned to kill anyway? He knew they were going to die (like everyone else in Gotham)...so why waste resources on them? He was hunting down and killing cops that hadn't been trapped below ground....so why would he waste time and resources to feed the armed men that would try to attack and stop him the first chance they got when he in his heart knew they would be dead in a few months from the nuke anyway?